9. A bond has the following features: • Coupon rate of interest : 8 percent • Pr
ID: 2663994 • Letter: 9
Question
9. A bond has the following features:• Coupon rate of interest : 8 percent
• Principal: $1000
• Term to maturity: 10 years
a. What will the holder receive when the bond matures?
b. If the current rate of interest on comparable debt is 12 percent, what should be the price of this bond? Would you expect the firm to call this bond? Why?
c. If the bond has a sinking fund that requires the firm to set aside annually with a trustee sufficient funds to retire the entire issue at maturity, how much must the firm remit each year for 10 years if the funds earn 9 percent annually and there is $10 million outstanding?
Explanation / Answer
a. On Maturity, Holder will receive the Face value of Bond ie $1000. b. N= 10-year Face value = FV = M= $1,000 INT=8% coupon rate = 8%*1,000 =$80 Nper = 10 Kd =Reqd rate of return = Debt rate=12%. We need to find Vb= value of Bond Vb = INT(PVIFA kd,N) + M*(PVIF kd,N). ie Vb = INT*[1/Kd - 1/(Kd*(1+Kd)^N)] + M*1/(1+Kd)^N ie Vb = 80*[1/12% - 1/(12%*(1+12%)^10] + 1,000/(1+12%)^10 ie Vb = 80*(8.33- 1/(12%*3.106)) + 1000/3.106 ie Vb = 80*(8.33-2.683) + 321.96 ie Vb = 80*5.65 + 321.96 ie Vb = $773.96 Firm will not call this bond as the current Int rate on Debt is 12% while firm is paying 8%. So if firm calls this bond, it will have to raise fresh debt at 12%. So firm is better off with paying 8% int. c. This is like calculating the annual payments of an annuity whose maturity value (FVA) is $10M & Int rate is i=9% with term of n=10 Yrs FV of Annuity is given by FVAn = PMT*FVIFAn,i ie FVA10 = PMT*FVIFA10,9% = PMT*[(1+i)^n - 1]/i ie FVA10 = PMT*[(1+9%)^10 - 1]/9% ie FVA10 = PMT*[2.3674 -1]/9% =15.193*PMT ie PMT = FVA10/15.193 = $10M/15.193 = $658,200.90 So an amount of $658,200.90 the firm has to set aside annually with a trustee to retire the entire issue at maturity.
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